Simplify Square Root of 78015

What is the square root of 78015 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√78015 = A√B

Unfortunately, the square root of 78015 cannot be simplified. Thus, here is the answer to the square root of 78015 in its simplest form:

√ 78015 = √ 78015

Here are two different methods we used to determine why the square root of 78015 cannot be simplified.

1) To be able to simplify the square root of 78015, one of the factors of 78015 other than 1 must be a perfect square. The factors of 78015 are 1, 3, 5, 7, 15, 21, 35, 105, 743, 2229, 3715, 5201, 11145, 15603, 26005, and 78015. Since none of these factors are perfect squares, the square root of 78015 cannot be simplified.

2) To be able to simplify the square root of 78015, all the prime factors of 78015 cannot be unique. When we did prime factorization of 78015, we found that 3 x 5 x 7 x 743 equals 78015. Since all the prime factors are unique, the square root of 78015 cannot be simplified.

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